Simple permutations: decidability and unavoidable substructures
classification
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keywords
simplepermutationscontainspermutationunavoidablealternationclassdecidability
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We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains an alternation or oscillation of length k.
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